Question

A vector $\underset{a}{\overset{}{\to }}$ has components 2p and 1 with respect to a reactangular cartesian system. The system is rotated through a certain angle about the origin in the counterclockwise direction . If with respect to the new system, $\underset{a}{\overset{}{\to }}$ has componets p+1 end 1 then.

Answer 1

$|\overrightarrow{a}|=|{\overrightarrow{a}}^1|$

$|2p\hat{i}+\hat{j}|=|(p+1)\hat{i}+\hat{j}|$

$\sqrt{4p^2+1}=\sqrt{(p+1{)}^2+1}$

$4p^2+1=(p+1{)}^2+1$

$2p=\pm (p+1)$

$(+)$

$2=p+1$

$p=1$

$(-)$

$2p=-p-1$

$3p=-1$

$p=\frac{-1}{3}$